Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = -5 and 5x + 2z = -3 r = ( 3 5 20)+1(8, 15 -20).

Q: Sell 1. What are the vertical asymptotes of y = 2tan(2x)?

A:

Q: 9-x I = = (x)u

A:

Q: When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the…

A: PV1.4=KPressure by stream =140lb/m2Volume expanded from  500in3 to 1200in3Formula for work done by…

Q: Given that lim f(x) = 0 x→a (a) lim lim g(x) = 0 x→a lim_h(x) = 1 x→a lim p(x) = ∞o x→a lim g(x) =…

A:

Q: The equation r(t) = (6 cos t)i + (4 sin t)j + (3t) k is the position of a particle in space at time…

A:

Q: determine the continuity of the function at a.

A: The objective of this question is to determine whether the function f(x) = 1/(x + 2) is continuous…

Q: Let f(x) = 2x + 5 and g(x) = 3x − 8, determine the domain of h (x) = g(x) = f(x) ○ (-∞, -)U (-7, ∞)…

A:

Q: 3x x-∞0 px+7 a) lim- = 2

A: (a) Gven,

Q: 1. Sketch one cycle of the following trigonometric equation, y = −2 sin(3x – 180°) + 1.

A:

Q: Sketch the region enclosed by the curves y = |x|and y = x² 2. Decide whether to integrate with…

A: Given that the region enclosed by the curves  and

Q: Calculate dif 17 P = V²R (R+r)2"

A:

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = 2x³ + y² +5, D = {(x, y) |…

A:

Q: A cardboard box without a lid is to have a volume of 16,384 cm³. Find the dimensions that minimize…

A: Let the length of the box ftLet the width of the box  ftLet height of the box  ft

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (−3t sint, -…

A:

Q: Find the value of x * in the interval [3, 6] that satisfies the equation b fro a in the Mean-Value…

A: To find all values of  in the interval  that satisfy the equation The given function is .

Q: Find all the values of x * in the interval [ – 5, 0] that satisfy the equation b js a f(x)dx = f(x *…

A: To find all values of  in the interval  that satisfy the equation in the Mean-Value Theorem for…

Q: Graph the given function on desmos.com and find the vertical and horizontal asymptotes. If none…

A:

Q: O For the function f(x) graphed on the right answer the following questions: lim f(x) = x→0+ Is…

A:

Q: Consider the following function. y = x2/7 (a) Find y'= f'(x). f'(x) = (b) Find the critical value.…

A:

Q: The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula…

A:

Q: A model for advertising response is given by Upper N left parenthesis a right parenthesis equals 12…

A: The objective of the question is to find the derivative of the function N(a) = 12,000 + 800 ln a at…

Q: 3. Using the derivative rules learned in section 3.2. 5 Let f(x) = 5x - 2x² and g(x) = 3ex − x−³ +…

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. X [cos = d.x…

A:

Q: Given f'(x) = x³ - 3x² and its graph, use the graph to determine the following. f(x) -4 -2 ✓…

A: Given and its graph is given below.To find the -value(s) where  has relative minima, and horizontal…

Q: Find the value of the graph of f(x) = -x² + 4 between x = -5 and x = 2

A:

Q: 1. Explain in full sentence(s) using the Intermediate Value Theorem why the equation 4x³ + 3x - 2 =…

A: The given equation is  on the interval [-2,2]As per the intermediate value theorem, if the function…

Q: On Exploration 4.3.3, what is a vertical asymptote for Question 1? Ox=0 x = π/8 x = 2n/3 Ox= π/2 x=л…

A: The objective of the question is to identify the vertical asymptote for a given function in…

Q: Evaluater(g(t)) using the Chain Rule: r(t) = (et, e³t, 1), g(t) = 3t — 2 #r(91)) = (100

A:

Q: Let f(x) = 3x³ – 6x - 2 Use the limit definition of the derivative to calculate the derivative of f:…

A:

Q: 3) [ dx (x²+3)7/2 =

A:

Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

A:

Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. [[₁ -…

A:

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim f(x) x+2 g(x) y 1 -1 -2 y =…

A: By using the graphs of  and their tangent lines at  to find .

Q: a.lim x₂0+x 1

A: we need to find the limit."As per the rules, we are supposed to answer the first question and the…

Q: Solve the initial value problem for r as a vector function of t. d²r Differential equation: वहर =…

A: The given diffferential equation is  and

Q: Find the derivative of the function.   y equals ln left parenthesis 3 x cubed minus x squared right…

A: The objective of the question is to find the derivative of the function y = ln(3x³ - x²).

Q: 9. X f(x) 2 -2 6 1 9 8 10 -4 15 3 The function f is continuous on the closed interval [2, 15] and…

A:

Q: Find the x>0 which minimizes 2*. Round to one decimal

A:

Q: Consider the following. f(-4)=-7, f(1) = 4 (a) Write the linear function f that has the given…

A:

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

A:

Q: At which value(s) for x does the graph of y = x³x² - 20x - 9 have horizontal tangent lines?

A:

Q: Find the area given by: 1 S In(x) dx 0 24 -1 -2 2 3

A:

Q: What is the instantaneous rate of change of f(x) √x 3 - X at x = 2?

A: (20) Given,

Q: 24 lim b7b+1 lim t 5 Calculate the following limits by direct substitution. (b-4)² (1 – t) (t + 5)…

A:

Q: Find a vector n normal to the plane with the equation 6z - n = (-5, (5x + 5y) = -1. >

A:

Q: According to Poiseuille's law, the speed S of blood through an artery of radius r at a distance x…

A:

Q: 5. A student was asked to find the equation of the tangent plane to the surface z = -y at the point…

A: The objective of the question is to identify the mistakes in the student's solution and to find the…

Q: Problem #3. Find the limit of the vector-valued function: lim (tln(t), n(), √In (t²)) Give your…

A:

Q: 3 X = = -1 X = = 0 12. Use the graph to answer the question. X = 1 X = 2 X = 3 X = 4 x = 5 X = = 6 x…

A: Given graph of a function isWe have to find the value(s) of x for which the function is…

Q: Show algebraically that ƒ(x) = |x − 1| = x = 1. J−x+1 x≤1 (x - 1 x > 1 is not differentiable at

A: Given,